用自然边界元法计算位势问题的近边界位势梯度

在二维位势问题中,位势导数场边界积分方程通常衍生出超奇异积分问题。通过新边界变量的替换消除了常规的位势导数边界积分方程中超奇异积分,推导出以位势梯度为边界量的自然边界积分方程。在常规的位势边界积分方程执行后,采用自然边界积分方程的边界元分析比常规边界元法得到更加准确的近边界位势梯度;算例显示了自然边界元法的有效性。     

Multi-Variable Non-Singular BEM for 2-D Potential Problems

A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations(BIEs) of the potential and its derivatives, where the nodal potential derivatives are considered independent of the nodal potential and flux. The system equation is solved to determine the unknown boundary potentials and fluxes, with high accuracy boundary nodal potential derivatives obtained from the solution at the same time. A modified Gaussian elimination algorithm was developed to improve the solution efficiency of the final system equation. Numerical examples verify the validity of the proposed algorithm.     

Study on the EM Scattering of Rivets on the Plate

The electromagnetic (EM) scattering by rivets on the conducting plate is studied for the first time by using electric field integral equation (EFIE) in conjunction with the moment method. The surfaces of the rivets and the plate are partitioned into triangular cells, the current distribution on the patches is represented by sub-domain type basis function, the EFIE is translated into matrix equation by the Galerkin method, then the current coefficient is obtained. The results show the properties of radar cross section (RCS) varying with the incident angle when there are rivets on the plate.     

量子概率和无限维分析国际会议论文集

本书是新加坡世界科技出版公司出版的《QP—PQ：量子概率和白噪声分析》系列丛书的第15卷，也是2001年3月在德国举行的“量子概率和无限维分析国际会议“的论文集。书中反映量子概率和无限维分析领域的最新研究成果，包括在量子随机积分、随机极限、量子远距传物和其他相关领域的新结果。     

从变换群的观点看Bertrand悖论

该文从变换群的观点讨论了Ｂｅｒｔｒａｎｄ悖论，指出了Ｂｅｒｔｒａｎｄ的几种几何概率分别是几种变换群下的不变量。     

球面分数次积分的Zygmund性质

设Ｓθ是ｎ维单位球面上的平移算子,对于ｐ≥１,Λｐ（α,β）是Ｚｙｇｍｕｎｄ类：Λｐ（α,β）＝｛ｆ（ｘ）Ｓθ（ｆ）－ｆｐ≤ｃｆθα（ｌｏｇ２πθ）β｝,０＜α≤１,β≥０．讨论了球面分数次积分的Ｚｙｇｍｕｎｄ性质．     

Holder积分不等式的几种证明方法

本文总结了Ｈｏｌｄｅｒ积分不等式的五种证明方法。     

圆口喷射器湍流流场数学模型及其最优设计

本文根据湍流射流和湍流边界层理论对圆喷嘴喷射器混合段湍流流场进行了研究,应用雷诺方程推导出喷射器混合段的基本方程和动量积分方程,用数学模型研究了喷射燃烧器,并对喷射器提出了一套最优设计公式。     

一类向量形式的积分—偏微分方程组的正则广义解

本文从具有双向流动的城乡人口系统的数学模型出发,讨论了一类向量形式的积分偏微分方程组,证明了该方程组的正则广义解的存在性。本文结果可为人口的预测提供数学方法。     

Riemann积分与Lebesgue积分的差别

本文指出Riemann积分与Lebesgue积分的本质区别在于空间的完备性上。区间(a,b)上所有Riemann可积函数所生成的空间R[a,b]是不完备的;而所有Lebesgue可积函数所生成的空间L[a,b]是完备的。